Should I replace "It would be possible that" and if so, why?

"Would be" is in the subjunctive mood, which means that it depends on something that may or may not have happened. In the original, it's possible that he's debating whether or not that's true. However, in the Wikipedia article, there is no reference that I see to an unknown possibility. As such, I think it makes more sense to replace "would be possible" with "is possible".

You'd have to say "would be possible" if it were this sentence, though:

"It would be possible that the manuscript … was written … in Jerusalem if the author lived in Jerusalem."

That said, we're splitting hairs about the original.